• ### Where are they now?

Offers solution to simple action stories when modelled by teacher, involving join and take-away in the range 1 – 5 using concrete materials and language and ‘make-all/count-all’ (count by ones) strategy

• ### Where to next?

Uses concrete materials to model and solve addition action stories (1-10) involving join or combine using ‘make all / count all’ or counting on from known (‘trusted’) number

• ### Purpose

Addition and subtraction are an important part of the skill set of a numerate person and are foundational skills for the other operations (multiplication and division) as well as for the larger body of mathematics.

• ### Building Addition and Subtraction skills:

The skill of adding and subtracting draws on all of the skills studied in the whole number section, and a failure to progress will generally indicate that one or more of these skills needs to be revisited.

Understanding addition and subtraction begins with the realisation that the total of a collection changes when items are added or removed. The key skill at this stage is still counting, as students will initially use a ‘make all- count all’ strategy. That is, they will either add or remove a specified number of items from their collection, and then count the new collection starting at one to find the new total. Language is an important element at this level – linkng the idea of adding and removing items from a collection should be linked with words such as add, plus, take, minus and subtract and difference*.

Once students are familiar enough with counting to ‘trust the count’ they will be able to add and subtract by counting on or back from the total. This is a very inefficient way of adding and subtracting however and as soon as students ‘trust the count’, they should start to explore patterns. These will be visual initially, through subitising and investigating the ‘part-part-whole’ nature of number using counters.

Part-part-whole knowledge begins with exploring the structure of all the numbers to 10 – understanding that four is two and two or three and one for example. Part-part-whole knowledge can then be extended to larger numbers through an understanding of the base 10 and place value system ultimately leading to efficient mental methods of adding and subtracting.

*Difference is an important idea as it leads to the understanding that add and subtract are just two different ways of looking at the same thing. Addition and subtraction should be taught as part of a single concept where possible.

### Activities and Assessments (Designed to move student on from step 2 to step 3)

Blank Beehives

Adapted from ‘Beehive’, Developing Efficient Numeracy Strategies Stage 1 page 34. NSW Department of Education and Training, Professional Support and Curriculum Directorate 2003

Focus: Emergent counting – that the total of a collection changes when items are added or removed, learning the terms ‘add’ and ‘take away’.

How: See Blank Beehives sheet

Part-part whole board

Focus: Identifying pairs of collections that add to make a given amount ( up to 10).

How:Place a known number of counters in the box on the board and then split them into two different groups. Count and discuss the two groups that make up the initial number and record by drawing a diagram or picture of the two groups. Repeat.

Ten frames

Adapted from ‘Ten Frames’, Developing Efficient Numeracy Strategies Stage 1 page 28. NSW Department of Education and Training, Professional Support and Curriculum Directorate 2003

Focus: Visualise collections up to 10 – in terms of the addition of two groups.

How:Provide each student with a ten-frame and 10 counters. Students take turns to throw a die (or spin a dot spinner), count the dots and place the corresponding number of counters onto the ten-frame. The exact number needed to complete the ten-frame must be rolled to finish. Students should be encouraged to state their current total (“how many do you have now altogether?”) as well as the number they need to make ten (“how many more do you need to make ten?”). The addition language inherent in the activity should also be made explicit (eg. “so three plus seven more will equal 10?”)

Try adding a rule where students fill one row of the ten-frame first. This helps to emphasise the structure of the “five” part of the number and also to see a larger number as being “five and something”, eg seven could be seen as five and two.

Ten Frame

Spinner

Memory-to-Ten game

Focus: Identifying pairs of numbers that add to make ten.

How:Use playing cards 1-9.  Place in a 3 x 4 grid pattern face down.  Children take turns, turning two cards over.  Do they make ten? If they do, child keeps the card and the next child takes their turn. Having counters or unifix cubes available for children to use may help to build initial understanding. Key questions to ask students are: “What is that number? ” and “How many more to make ten?”